How to only show related field picklist values of related re

I have a Customer who has an employee called Matt. I also have a Customer who has an employee called Roger.

I can also add Websites, so I created a relationship between my Website and Customer. Because I want to select a contactperson, I created a related field with "Related Object" Customer and "Related Field" Employees. I changed the "Style" from Selector to Picklist.

When I try to select Employees with the selector it only shows Matt, but when I try selecting Employees with my picklist it shows both Matt and Roger. (The Customer has been set.) How could I prevent showing these Employees that aren't an Employee of Customer?